Finding Lengths of Springs with Three Identical Masses

[Moninder]

Homework Statement

Three identical 6.00kg masses are hung by three identical springs, as shown in the figure. Each spring has a force constant of 8.50kN/m and was 11.0cm long before any masses were attached to it. How long is each spring when hanging as shown? (Hint: First isolate only the bottom mass. Then treat the bottom two masses as a system. Finally, treat all three masses as a system.)

Homework Equations

F=-ma
F=-kx

The Attempt at a Solution

I started with the bottom block.
-ma=-kx
(6.00kgx9.8m/s^2)/-(8.50kN/m)=x
x=6.92m? and then i added 0.11m
and its still wrong
I also took the F=ma and divided by 1000 to get into(0.0588) kN and then divided it by 8.50kN and then dded .11m and still wrong

I need to find all three block eventually

 

[AJ Bentley]

That can't be answered without the diagram.

 

[Moninder]

This is how it is from top to bottom
Ceiling
-
spring
-
block
-
spring
-
block
-
spring
-
block

 

[Chestermiller]

Homework Statement

Three identical 6.00kg masses are hung by three identical springs, as shown in the figure. Each spring has a force constant of 8.50kN/m and was 11.0cm long before any masses were attached to it. How long is each spring when hanging as shown? (Hint: First isolate only the bottom mass. Then treat the bottom two masses as a system. Finally, treat all three masses as a system.)

Homework Equations

F=-ma
F=-kx

The Attempt at a Solution

I also took the F=ma and divided by 1000 to get into(0.0588) kN and then divided it by 8.50kN and then dded .11m and still wrong

What was your answer from doing the calculation this way, and how do you know it was wrong?

 

[Moninder]

For the bottom spring I got 0.1169m
Middle Spring 0.3376m
Top spring 0.35075m

I put it in an online program

 

[Moninder]

Still need help

 

[Doc Al]

I started with the bottom block.
-ma=-kx
(6.00kgx9.8m/s^2)/-(8.50kN/m)=x
x=6.92m?

Note that the spring constant is in kN/m, not N/m.

 

[Moninder]

Note that the spring constant is in kN/m, not N/m.

Yes I know, check my 3 answers i posted, they are with converting the kN

 

[Doc Al]

For the bottom spring I got 0.1169m

Looks OK.

Middle Spring 0.3376m
Top spring 0.35075m

Show how you got these last two.

 

[Moninder]

Looks OK.

Show how you got these last two.

I added the weights together
Mg=kx
((6+6)9.8)/(8500N/m) + .22 m =middle spring
Top spring
((6+6+6)9.8)/(8500N/m) + 0.33m

 

[Doc Al]

I added the weights together
Mg=kx
((6+6)9.8)/(8500N/m) + .22 m =middle spring
Top spring
((6+6+6)9.8)/(8500N/m) + 0.33m

Ah... But they all start with an unstretched length of 0.11m.

 

[Moninder]

Ah... But they all start with an unstretched length of 0.11m.

Yes, i did add in the unstrecthed length?

 

[Doc Al]

Yes, i did add in the unstrecthed length?

For the middle spring you added in twice the unstretched length; for the top spring you added three times the unstretched length.

Each spring has a total length equal to its unstretched length (0.11m for each) plus the amount of stretch (which varies).

 

[Moninder]

Why would i not add in 2 lengths because the middle spring is also carrying the bottom spring

 

[Doc Al]

Why would i not add in 2 lengths because the middle spring is also carrying the bottom spring

How does that affect its unstretched length?

 

[Moninder]

Oh now i get it, i should just only add in 1 unstrecthed length because I am only calculating for 1 spring

 

[Doc Al]

Oh now i get it, i should just only add in 1 unstrecthed length because I am only calculating for 1 spring

Right.

 

[Moninder]

Thank you